Asymptotic estimates for the solution of stochastic differential equations driven By G-Brownian motion

Abstract

In this paper, we give four results of asymptotic estimates for the solution of stochastic differential equations driven by G-Brownian motion, which have different convergence rates under different assumptions. One of them can be considered as a Law of the Iterated Logarithm of the solution of G-SDEs under nonlinear conditions.

Keywords:

• Nonlinear expectation
• G-Brownian motion
• stochastic differential equations
• law of the iterated logarithm

AMS Subject Classification:

• 65C30

Acknowledgements

The authors would like to thank the editor and two anonymous referees for their careful reading and helpful suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Luo’s research is partially supported by National Science Foundation of China, ‘Research Fund for International Young Scientists’ [grant number 11550110184]; National Natural Science Foundation of China [grant number 11601282]; Shandong Provincial Natural Science Foundation [grant number ZR2016AQ10].